Decentralized H_∞ controller design for large-scale systems: a matrix inequality approach using a homotopy method

This paper considers a decentralized H_∞ control problem for large-scale systems consisting of a number of interconnected subsystems with the information structure constraints which are compatible with the subsystems. The H_∞ control specification is imposed on the transfer function from the disturbance input to the controlled output of the overall closed-loop system. The decentralized H_∞ control problem is reduced to a feasibility problem of a bilinear matrix inequality (BMI). To solve the BMI, an algorithm is proposed using the idea of the Homotopy method, where the interconnections between subsystems are increased gradually from zeros to the given magnitudes. The case where polytopic perturbations exist in the interconnections is also treated.